Answer:
There is a 9.6% probability that a person is diagnosed as having cancer.
Step-by-step explanation:
In this problem, we have these following probabilities:
A 5% probability that an adult over 40 has cancer.
This also means that:
There is a 95% probability that an adult over 40 does not have cancer. (Since either the adult has cancer or does not have cancer, and the sum of the probabilities is 100%).
A 78% probability of a person that has cancer being diagnosed,
A 6% probability of a person that does not have cancer being diagnosed.
What is the probability that a person is diagnosed as having cancer?
[tex]P = P_{1} + P_{2}[/tex]
[tex]P_{1}[/tex] is the probability of those who have cancer being diagnosed. So it is 78% of 5%. So
[tex]P_{1} = 0.05*0.78 = 0.039[/tex]
[tex]P_{2}[/tex] is the probability of those who do not have cancer being diagnosed. So it is 6% of 95%. So
[tex]P_{1} = 0.06*0.95 = 0.057[/tex]
So
[tex]P = P_{1} + P_{2} = 0.039 + 0.057 = 0.096[/tex]
There is a 9.6% probability that a person is diagnosed as having cancer.
we apply 35% of a drug at the morning and 25% of the same drug at the afternoon. if in the evening 28 mL of the drug is left. how many milliliters are we applying during the whole day?
Answer:
we are applying 70 ml during the whole day
Step-by-step explanation:
First, it is necessary to calculate the percentage of the drug that is left in the evening. This is calculated as:
100% - (35% + 25%) = 100% - 60% = 40%
Because, 35% is the percentage of the drug apply at the morning and 25% is percentage of the drug apply at afternoon.
Then, 40% is the percentage of the drug that is left in the evening and it is equivalent to 28 mL. So, the milliliter that we apply during the whole day are the milliliters equivalent to the 100%. We can calculate this by a rule of three as:
40% -------------------- 28 mL
100% ------------------- X
Where X are the milliliters that we apply during the whole day. Solving for X, we get:
[tex]X=\frac{100*28}{40}=70 mL[/tex]
Use the patterns you found to predict whether each set of lengths below will form a triangle. If a set will form a triangle, state whether the triangle will be acute, obtuse, or right. Justify your conclusion. a. 5 cm, 6 cm, and 7 cm b. 2 cm, 11 cm, 15 cm c. 10 cm, 15 cm, 20 cm d. 10 cm, 24 cm, 26 cm e. 1 cm, 3 cm, 9 cm f. 2 cm, 10 cm, 11 cm Core Connections, Course } 412
Answer with Step-by-step explanation:
We have to find given length set form a triangle and find the type of triangle acute, obtuse or right.
If sum of length of any two sides is greater than the length of third side then the given side length form a triangle otherwise not.
a.5 cm, 6 cm and 7 cm
[tex]5+6=11cm > 7cm[/tex]
Hence, given set of side length form a triangle.
[tex]5^2+6^2=25+36=61 >7^2=49[/tex]
Hence, given triangle is acute triangle.
b.2 cm,11 cm,15 cm
[tex] 2+15=17 cm > 11 cm[/tex]
Hence, given side length set form a triangle.
[tex]2^2+11^2=4+121=125 < (15)^2=225[/tex]
Hence, the triangle is an obtuse triangle.
c.10 cm,15 cm,20 cm
[tex]10+15=25 cm >20 cm[/tex]
Hence, given set of length side form a triangle.
[tex](10)^2+(15)^2=225 >(20)^2=400[/tex]
Hence, the triangle is an acute triangle .
d.10 cm,24 cm,26 cm
[tex]10+24=34 cm > 26 cm[/tex]
Hence, given set of side length form a triangle.
[tex](10)^2+(24)^2=676=(26)^2=676[/tex]
Hence, the triangle forms a right triangle.
e.1 cm,3 cm, 9 cm
[tex]1+9=10 cm > 3 cm[/tex]
Hence, the given set of side length forms a triangle.
[tex]1^1+3^2=10<9^2=81[/tex]
Hence, the triangle is an obtuse triangle.
f.2 cm, 10 cm,11 cm
[tex]2+10=12 cm > 11cm[/tex]
Hence, the given set of side length set forms a triangle.
[tex]2^2+(10)^2=104<(11)^2=121[/tex]
Hence, the triangle is an obtuse triangle.
1/250 : 2 = 1/150 : x
Answer:
The value of x is [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Given,
[tex]\frac{1}{250}:2=\frac{1}{150}:x[/tex]
[tex]\frac{1/250}{2}=\frac{1/150}{x}[/tex]
[tex]\frac{1}{500}=\frac{1}{150x}[/tex]
By cross multiplication,
[tex]150x = 500[/tex]
[tex]x=\frac{500}{150}=\frac{500\div 50}{150\div 50}=\frac{10}{3}[/tex]
A nurse is preparing to administer dextrose 5% water (D5W) 250 ml IV to infuse over 2 hr. The nurse should set the IV pump to deliver how many ml/hr?
Answer:
The nurse should set the IV pump to deliver 125 ml/hr.
Step-by-step explanation:
The problem states that a nurse is preparing an IV pump to administer 250ml over 2 hours. So how many ml should be administered each hour?
This problem can be solved by this following rule of three.
250 ml - 2 hours
x ml - 1 hours
[tex]2x = 250[/tex]
[tex]x = \frac{250}{2}[/tex]
[tex]x = 125[/tex]ml.
The nurse should set the IV pump to deliver 125 ml/hr.
To determine the intermittent IV infusion rate, divide the total volume of the fluid (dextrose 5% water) by the total time of infusion. Here, it would be 250 ml divided by 2 hours, which equals 125 ml per hour.
Explanation:To determine how many ml per hour a nurse should set the IV pump to deliver dextrose 5% water (D5W), you should divide the total volume by the total time. In this case, the total dextrose volume is 250 ml and it should be infused over 2 hours. Using the formula:
Total Volume / Total Time = ml per hour250 ml / 2 hr = 125 ml/hrSo, the nurse should set the IV pump to deliver 125 ml per hour of dextrose.
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Melissa is 29 meters below the surface. After swimming 12 minutes she rises upward 15 meters. What is her final depth?
Answer:
The final depth of Melissa is 14 meters below the surface
Step-by-step explanation:
In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.
In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position(positive depth) and below the surface is the negative directions(negative depth).
The problem states that Melissa is 29 meters below the surface. So, her initial position is 29 meters in the negative direction, so it is equal to -29.
Then, the problem states that Melissa rises upward 15 meters. Upward is the positive direction, so she moved to the positive direction. It means that we are going to do -29+15 = -14 meters.
It means that the final depth of Melissa is 14 meters below the surface
Solve the system of inequalities by graphing.
Answer:
infinitely many
Step-by-step explanation:
there were too many lines
Answer:
The correct option is D) Infinitely many.
Step-by-step explanation:
Consider the provided graph.
The system of equation has the solution at the point where the line intersects.
Now consider the graph of the equation 2x = 2y-6 and y = x+3
By observing the graph it can be concluded that the graph of 2x = 2y-6 and y = x+3 has the same line.
A system of equation have infinitely many solutions if each equations refers to the same line.
Since 2x = 2y-6 and y = x+3 refer the same line. The system has infinitely many solutions.
Hence, the correct option is D) Infinitely many.
Which expression is equivalent to this one:
[tex]\frac{2}{3}[/tex] x 6 + [tex]\frac{2}{3}[/tex] x s
A) 6([tex]\frac{2}{3}[/tex] + s)
B) s(6+[tex]\frac{2}{3}[/tex])
C) [tex]\frac{2}{3}[/tex](6+s)
D) [tex]\frac{2}{3}[/tex] x (6+[tex]\frac{2}{3}[/tex]) x s
Answer:
C) [tex]\dfrac{2}{3}(6+s)[/tex]
Step-by-step explanation:
The distributive property lets you factor out the common factor of 2/3. The result is ...
[tex]\dfrac{2}{3}(6+s)[/tex]
What is the ordinal number
just before 152nd?
Answer:
151.
Step-by-step explanation:
50th or Fiftieth Ordinal numbers are just numbers that identify the order of things: Thus having 151 coming before 152.
The ordinal number just before 152nd is 151st.
Explanation:The ordinal number just before 152nd is 151st. Ordinal numbers are used to indicate position or order, and they are formed by adding the suffix '-st' to the cardinal number. In this case, the cardinal number 152 is changed to the ordinal number 152nd by adding '-nd' suffix. To find the ordinal number just before 152nd, we go one step back and change the '-nd' suffix to '-st', resulting in 151st.
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Choose all the numbers that are part of Integers.
1
0
-3
5/6
-23
Answer:
all except 5/6
Step-by-step explanation:
All of the numbers listed are in the set of integers, except for the fraction 5/6. It is a rational number, but not an integer.
___
If by "part of integers" you mean that the number can be multiplied by some integer value to make an integer, then 5/6 is "part of 5". It is 1/6 of the integer 5.
N1
N2
N3
N4
[[[(2x4)x3]/12] x (2x6)]/12 = ?
Answer:
2
Step-by-step explanation:
Rewriting the expression we have:
[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}[tex]
Then we have the next step by step solution, starting by the insider parentheses:
[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}=\dfrac{\dfrac{[8\times 3]}{12}\times(12)}{12}=\dfrac{\dfrac{24}{12}\times(12)}{12}=\dfrac{2\times(12)}{12}=\dfrac{24}{12}=2[/tex]
Zene decides to canoe 7 miles upstream on a river to a waterfall and then canoe back. The total trip (excluding the time spent at the waterfall) takes 8 hours. Zene knows she can canoe at an average speed of 3 miles per hour in still water. What is the speed of the current?
Answer:
V = 1.94 mi/h
Step-by-step explanation:
mark me brainliest plz
The speed of the current is approximately 0.5 mph.
How to calculate the speed of the river's current?Let's assume the speed of the current is "c" mph. Zene's upstream speed is (3 - c) mph and downstream speed is (3 + c) mph.
The time taken for the upstream trip is 7 / (3 - c) hours, and the time for the downstream trip is 7 / (3 + c) hours.
Since the total trip time is 8 hours, we can set up the equation:
7 / (3 - c) + 7 / (3 + c) = 8
Solving this equation, we find the speed of the current is approximately 0.5 mph.
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You are evaluating the risks associated with a construction project. Through careful analysis you have developed a list of the following risks, probabilities those risks will happen, and the costs associated with them if they occur.
25% chance of Snowmaggedon which will delay the project at a cost of $35,000
10% chance of cost of construction materials dropping saving the project $70,000
10% probability a labor strike will occur delaying the schedule with a cost of $40,000
80% chance of new regulations mandated calling for higher inspection standards which will cost an additional $15,000 to mitigate
What is the EMV of this project?
Answer:
The EMV of this project is -17,500
Step-by-step explanation:
The EMV of the project is the Expected Money Value of the Project.
This value is given by the sum of each expected earning/cost multiplied by each probability.
So, in our problem
[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4}[/tex]
The problem states that there is a 25% chance of Snowmaggedon which will delay the project at a cost of $35,000. Since this is a cost, [tex]P_{1}[/tex] is negative.
[tex]P_{1} = 0.25*(-35,000) = -8,750[/tex]
There is a 10% chance of cost of construction materials dropping saving the project $70,000. A saving is an earning, so [tex]P_{2}[/tex] is positive
[tex]P_{2} = 0.10*70,000 = 7,000[/tex]
There is a 10% probability a labor strike will occur delaying the schedule with a cost of $40,000.
[tex]P_{3} = 0.10*(-40,000) = -4,000[/tex]
There is a 80% chance of new regulations mandated calling for higher inspection standards which will cost an additional $15,000 to mitigate
[tex]P_{4} = 0.80*(-15,000) = -12,000[/tex]
[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4} = -8,750 + 7,000 - 4,000 - 12,000 = -17,500[/tex]
The EMV of this project is -17,500
The following data represent the ages of award winners for best actor and best actress in a leading role for the 20 years from 1985 to 2004. Answer parts (a)minus(b) below. Full data set Best Actor Ages Best Actress Ages 40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51 33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25 (a) Construct an ordered back to back stem-and-leaf display.
Answer:
[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]
Step-by-step explanation:
You are given the set of data
40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51 33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25
First, rewrite it in ascending order:
22 24 25 25 25 26 27 32 32 32 33 33 33 34 35 35 37 37 37 38 39 39 40 43 43 44 44 45 46 48 49 51 52 52 53 54 60 61 64 70
The first gigit of each number write into the stem column and the second digit of each number write into the leaf column. So, the stem-and-leaf display is
[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]
Here is the back - to - back stem and leaf plot of the data :
LEAF ___________ stem _________ LEAF
Best actor age_____ | | ___ Best actress age
5, 6, 7 ___________| 2 | _______ 2, 4 5, 5
2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9
0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9
1, 2 _____________ | 5 | ___________ 2, 3
0, 1, 4 ___________ | 6 | ______________
________________ | 7 | _____________ 0
Given the data :
Best actor :
40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51
Best actress :
33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25.
Stem and leaf plot involves an ordered arrangement of values by seperating the the highest placed digit of each value into stems and the other digits into leaves.
Ordering the data :
Best actor :
25, 26, 27, 32, 32, 33, 35, 37, 37, 37, 38, 40, 44, 45, 48, 51, 52, 60, 61, 64
Best actress :
22, 24, 25, 25, 32, 33, 33, 34, 35, 39, 39, 43, 43, 44, 46, 49, 52, 53, 54, 70
The values range from :
22 to 70 ;
Hence, our stems will inculude : 2, 3, 4, 5, 6 and 7
LEAF ___________ stem _________ LEAF
Best actor age_____ | | ___ Best actress age
5, 6, 7 ___________| 2 | _______ 2, 4 5, 5
2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9
0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9
1, 2 _____________ | 5 | ___________ 2, 3
0, 1, 4 ___________ | 6 | ______________
________________ | 7 | _____________ 0
KEY : 2 | 2 = 22
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Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta. 2cos2(θ)−1 2 c o s 2 ( θ ) − 1 = nothing
The expression [tex]\(2\cos^2(\theta) - 1\)[/tex] where θ is the lowercase Greek letter theta gives [tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex].
The expression is [tex]\(2\cos^2(\theta) - 1\)[/tex].
Explanation:
1. 2: This is a coefficient that scales the result of the trigonometric function [tex]\(\cos^2(\theta)\)[/tex]. It simply doubles the value of the cosine squared term.
2. [tex]\(\cos^2(\theta)\)[/tex]: This is the square of the cosine of the angle [tex]\(\theta\)[/tex].
The cosine function cos takes an angle as input and returns the ratio of the adjacent side to the hypotenuse in a right triangle with that angle.
3. -1: This is a constant that is subtracted from the result of [tex]\(2\cos^2(\theta)\)[/tex]. Subtracting 1 shifts the trigonometric value downward by one unit on the y-axis.
Add 1 to both sides
[tex]2cos^2(\theta) =1[/tex]
Divide by 2 on both sides
[tex]cos^2(\theta) =1/2[/tex]
Take the square root of both sides
[tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex]
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The expression in question pertains to the conservation of momentum in physics, where trigonometric identities can simplify the calculation of particle velocities and directions after a collision. The included equations and concepts such as the conservation of momentum along an axis and the Pythagorean Theorem are essential components for solving problems in high school physics.
Explanation:The expression 2cos2(θ)−1, where θ is the lowercase Greek letter theta, can be related to conservation of momentum in physics problems, particularly when analyzing collisions in two dimensions. Using trigonometric identities, such as tan θ = sin θ / cos θ, can be a useful technique in simplifying expressions and solving for unknown variables in mechanical physics.
In the context of conservation of momentum, equations may involve cosines and sines of angles representing the directions of particle velocities before and after a collision. For instance, if the scenario requires that the momentum along the x-axis be conserved, substituting sin θ / tan θ for cos θ could lead to simplifications where terms cancel out. A condition such as μ v2 cos(θ1−θ2)= 0 might imply that either the coefficient of friction μ is zero or the velocity component along the x-axis is zero, hence no momentum is transferred in that direction.
It is important to note that inverting mathematical functions is a common approach to solving equations in physics. Like in trigonometry, it may be necessary to 'undo' a function to isolate a variable, as shown in the example involving the Pythagorean Theorem to solve for side length of a triangle.
solve the linear programming problem by graphing. graph the feasible region, list the extreme points and identify the maximum value of Z. please list the equations of the lines that form the feasible region
Minimize z=4x+y
subject to
2x+4y>= 20
3x+2y<=24
x,y>=0
Answer:
The minimum value of objective function is 5 at x=0 and y=5.
Step-by-step explanation:
The given linear programming problem is
Minimize [tex]z=4x+y[/tex]
Subject to constraints
[tex]2x+4y\geq 20[/tex] .... (1)
[tex]3x+2y\leq 24[/tex] .... (2)
[tex]x,y\geq 0[/tex]
The related line of both inequalities are solid lines because the sign of inequalities are ≤ and ≥. It means the points lie on related line are included in the solution set.
Check both inequalities by (0,0).
[tex]2(0)+4(0)\geq 20[/tex]
[tex]0\geq 20[/tex]
This statement is not true. So, the shaded region of inequality (1) will not contain the origin.
[tex]3(0)+2(0)\leq 24[/tex]
[tex]0\leq 24[/tex]
This statement is true. It means the shaded region of inequality (2) will contain the origin.
[tex]x,y\geq 0[/tex] means first quadrant.
The common shaded region is feasible region. The vertices of feasible region are (0,5), (0,12) and (7,1.5).
Calculate the value of objective function at these vertices.
For (0,5)
[tex]z=4(0)+(5)=5[/tex]
For (0,12)
[tex]z=4(0)+(12)=12[/tex]
For (7,1.5)
[tex]z=4(7)+(1.5)=29.5[/tex]
Therefore the minimum value of objective function is 5 at x=0 and y=5.
From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21 21 21
Answer:
Step-by-step explanation:
We know that between 1 to 10 there are 5 even and 5 odd numbers.
We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards
Let´s check all this combinations
Case 1: When all 4 numbers are even:
We are going to take 4 of the 5 even numbers in the box so we have
[tex]5C4=5[/tex]
Case 2: When all 4 numbers are odd:
We are going to take 4 of the 5 odd numbers in the box, so we have
[tex]5C4=5[/tex]
Case 3: When 2 are even and 2 are odd:
We are giong to take 2 from 5 even and odd cards in the box so we have
[tex]5C2 * 5C2[/tex]
Remember that we obtain the probability from
[tex]\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}[/tex]
So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:
We are taking 4 of the 10 cards:
[tex]10C_4=210[/tex]
Hence we have that the probability that their sum is even
[tex]\frac{5+5+100}{210}=\frac{11}{21}[/tex]
Final answer:
To find the probability that the sum of the four cards drawn is even, we can break down the problem into two cases: drawing all four even-numbered cards or drawing two even-numbered cards and two odd-numbered cards. Using the multiplication rule, we calculate the probability for each case and add them together to get the total probability.
Explanation:
Total Number of Possible Outcomes: If we draw four cards from a box containing cards numbered 1 to 10, the total number of ways to do this is given by the combination formula,
resulting in 10!/4!(10-4)! = 210 possible outcomes.
Number of Ways to Get an Even Sum:
For the sum of the numbers on the four drawn cards to be even, there are two cases to consider:
1. All four cards have even numbers: There are 5 even-numbered cards out of 10, and we need to choose 4 of them. The number of ways to do this is =5.
2. Three cards have odd numbers, and one card has an even number:
There are 5 odd-numbered and 5 even-numbered cards.
We need to choose 3 odd-numbered cards out of 5 and 1 even- numbered card out of 5.
The number of ways to do this is =50
Total Number of Ways for an Even Sum:
Adding the possibilities from both cases, we have a total of 5 + 50 = 55 ways to get an even sum.
The probability is then calculated as the ratio of the number of ways to get an even sum to the total number of possible outcomes:
Probability = Number of Ways to Get an Even Sum/Total Number of Possible Outcomes = 55/210= 11/42
Therefore, the probability that the sum of the numbers on the four drawn cards is even is 11/42.
A store asked 250 of its customers how much they spend on groceries each week. The responses were also classified according to the gender of the customers. We want to study whether there is a relationship between amount spent on groceries and gender. A meaningful display of the data from this study would be:
(A) side-by-side boxplots
(B) a pie chart
(C) a histogram
(D) a scatterplot
(E) a two-way table
Answer:
A boxplot offers us information that can be used to compare two variables. In particular, if one variable is quantitative and the other variable is qualitative, a boxplot is generated for each category of the qualitative variable. Therefore, through this graph it is possible to analyze the relationship between the amount of money spent on food and the gender of the person.
A circular diagram offers information for a single variable, especially of a qualitative type.
A histogram offers us information for a single variable, especially quantitative type.
A relational analysis between two variables could be done using options (D) or (E), however one of the variables of interest is of qualitative type and the other is of quantitative type, so the scatterplot and the two-way table.
Step-by-step explanation:
If an injectable solution contains 25μg of a dug substance in each 0.5 mL, how many milliliters would be required to provide a patient with 0.25 mg of the drug substance?
Answer:
5mL would be required to provide a patient with 0.25 mg of the drug substance.
Step-by-step explanation:
The problem states that an injectable solution contains 25μg of a dug substance in each 0.5 mL, and asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance.
So, the first step is the conversion of 25ug to mg, since the problem asks the answer in mg.
Each mg has 1000ug. So
1mg - 1000ug
xmg - 25ug
1000x = 25
[tex]x = \frac{25}{1000}[/tex]
x = 0.025 mg
It means that each 0.5mL of the solution contains 0.025mg of the drug. How many milliliters would be required to provide a patient with 0.25 mg of the drug substance.
0.5mL - 0.025mg
xmL - 0.25mg
0.025x = 0.5*0.25
[tex]x = \frac{0.5*0.25}{0.025}[/tex]
x = 10*0.5
x = 5mL
5mL would be required to provide a patient with 0.25 mg of the drug substance.
Final answer:
To provide a patient with 0.25 mg of a drug substance, 5 mL of the injectable solution is required when the solution concentration is 25μg per 0.5 mL.
Explanation:
If an injectable solution contains 25μg of a drug substance in each 0.5 mL, the question asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance. First, it is important to convert 0.25 mg to micrograms (μg) because the concentration of the drug is given in micrograms. Knowing that 1 mg = 1000 μg, we have:
0.25 mg = 0.25 × 1000 μg = 250 μg.
Next, if 25 μg is in 0.5 mL, we find how many times 25 μg goes into 250 μg to determine the volume needed:
250 μg / 25 μg/mL = 10 times
Since 25 μg is contained in 0.5 mL:
10 × 0.5 mL = 5 mL.
Therefore, 5 mL of the injectable solution is required to provide a patient with 0.25 mg of the drug substance.
Successful implementation of a new system is based on three independent modules. Module 1 works properly with probability 0.9, Module 2 works properly with probability 0.84, and Module 3 works properly with probability 0.65. What is the probability that at least one of these three modules will fail to work properly?
Answer:
The probability is 0.5086
Step-by-step explanation:
The probability P that at least one of these three modules will fail to work properly is calculated as:
P = 1 - P'
Where P' is the probability that all the modules works properly. So, P' os calculated as:
P' = 0.9 * 0.84 * 0.65
P' = 0.4914
Because 0.9 is the probability that module 1 works properly, 0.84 is the probability that module 2 works properly and 0.65 is the probability that module 3 works properly.
Finally, the probability P that at least one of these three modules will fail to work properly is:
P = 1 - 0.4914
P = 0.5086
Dexter's dad runs a toy store. His current yearly sales report shows that he sold 4,694 toys in the last three months. If the store made an average profit of $2.95 on each toy, what is the total profit in the three months? A. $12,647.25 B. $13,847.30 C. $14,007.29 D. $15,291.42
Answer:
$13847.30, Option B
Step-by-step explanation:
sold toys = 4694
average profit on each toy = $2.95
total profit in the three months = $2.95 * 4694 = $13847.30
Which expression is equivalent to 4-2/2-3
A -16
B -8
C 8
D 16
Answer:
0
Step-by-step explanation:
4 - 2/2 - 3 =
Follow the correct order of operations. Start with the division.
= 4 - 1 - 3
Now do subtractions from left to right in the order they appear.
= 3 - 3
= 0
Answer: 0
In the Holiday Shop the manager wants 20% of the total inventory in the stockroom and the rest displayed on the floor. After meeting these instructions, you placed $35,000 of inventory in the stockroom. What is the dollar amount of the inventory on the selling floor?
Total Inventory
Inventory in the stockroom
Inventory on the selling floor
Answer:
Total inventory: $175,000
Inventory in the stockroom: $35,000.
Inventory on the selling floor: $140,000.
Step-by-step explanation:
Let x be the the total inventory.
We have been given that in the Holiday Shop the manager wants 20% of the total inventory in the stockroom. You placed $35,000 of inventory in the stockroom.
We can set an equation such that 20% of x equals $35,000.
[tex]\frac{20}{100}\cdot x=\$35,000[/tex]
[tex]0.20x=\$35,000[/tex]
[tex]\frac{0.20x}{0.20}=\frac{\$35,000}{0.20}[/tex]
[tex]x=\$175,000[/tex]
Since $35,000 of inventory in the stockroom, so we will subtract $35,000 from $175,000.
[tex]\text{Amount of the inventory on the selling floor}=\$140,000[/tex]
Therefore, $140,000 of the inventory on the selling floor.
A buoy floating in the ocean is bobbing in simple harmonic motion with period 7 seconds and amplitude 6ft. Its displacement d from sea level at time t=0 seconds is -6ft, and initially it moves upward. (Note that upward is the positive direction.)
Give the equation modeling the displacement d as a function of time t.
Answer:
d = 6 sin(2π/7 t + 3π/2)
Step-by-step explanation:
Equation for simple harmonic motion is:
d = A sin(2π/T t + B) + C
where A is the amplitude,
T is the period,
B is the horizontal shift (phase shift),
and C is the vertical shift.
Given that A = 6, T = 7, and C = 0:
d = 6 sin(2π/7 t + B)
At t = 0, the buoy is at d = -6:
-6 = 6 sin(2π/7 (0) + B)
-1 = sin(B)
3π/2 = B
d = 6 sin(2π/7 t + 3π/2)
Notice you can also use cosine instead of sine and get a different phase shift.
d = 6 cos(2π/7 t + π)
You can even use phase shift properties to simplify:
d = -6 cos(2π/7 t)
Any of these answers are correct.
The equation modeling the displacement d of the buoy as a function of time is d(t) = 6 * sin(2π/7 * t) - 6.
Explanation:To model the displacement d of the buoy as a function of time t, we can use the equation:
d(t) = A * sin(2π/T * t) + C
where A is the amplitude, T is the period, t is the time, and C is the vertical displacement at t = 0 seconds.
In this case, the amplitude A is 6ft, the period T is 7 seconds, and the vertical displacement at t = 0 seconds C is -6ft and the buoy initially moves upward. Therefore, the equation modeling the displacement as a function of time is:
d(t) = 6 * sin(2π/7 * t) - 6
Learn more about Simple Harmonic Motion here:https://brainly.com/question/35900466
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For a normal distribution with mean equal to 31.5 and standard deviation equal to 11, what is the area under the curve that is between 35 and 45?
Answer:
The area is given by the following integral: [tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx[/tex], which can be approximated by: 0.265313
Step-by-step explanation:
A normal distribution is defined as:
[tex]f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}[/tex]
, where the greek letter sigma stands for the standard deviation and mu for the mean. Since in our problem we have a mean = 31.5 and a standard deviation = 11, then we can write this function as:
[tex]f(x)=\frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}}[/tex]
Now, we need to find the area below this function, between 35 and 45, and in order to do this, we need to integrate the function. The normal distribution does not has an exact closed form integral, therefore we will have to solve the integral in a software that allows for numerical calculations (I used the online software Wolfram|Alpha).
[tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx =0.265313[/tex]
A student club has seven members. 3 are to be chosen to go together to a national meeting. A) how many distinct groups of 3 can be chosen? B) if the student club contains 4 men and 3 women, how many distinct groups of 3 contain two men and one woman?
Answer:
1) 35 distinct groups can be formed.
2) 18 distinct groups can be formed containing 2 men and 1 woman.
Step-by-step explanation:
The no of groups of 3 members that can be chosen from 7 members equals no of combinations of 3 members that can be formed from 7 members.
Thus no of groups =
[tex]n=\binom{7}{3}=\frac{7!}{(7-3)!\times 3!}=35[/tex]
thus 35 distinct groups can be formed.
Part b)
Now since the condition is that we have to choose 2 men and 1 women to form the group
let A and B be men member's of group thus we have to choose 2 member's from a pool of 4 men which equals
[tex]\binom{4}{2}=\frac{4!}{(4-2)!\times 2!}=6[/tex]
Let the Woman member be C thus we have to choose one woman from a pool of 3 women hence number of ways in which it can be done equals 3.
thus the group can be formed in [tex]6\times 3=18[/tex] different ways.
Mia Salto wishes to determine how long it will take to repay a
$18,000 loan given that the lender requires her to make annualend-of-year installment payments of
$4,309
.
a. If the interest rate on the loan is
15%,
how long will it take for her to repay the loan fully?
b. How long will it take if the interest rate is
12%?
c. How long will it take if she has to pay
19%
annual interest?
d. Reviewing your answers in parts
a,
b,
and
c,
describe the general relationship between the interest rate and the amount of time it will take Mia to repay the loan fully.
Answer: a. 10.2 years
b. 12.6 years
c. 8.2 years
d. n = ln 4.1773/ln (1+r)
Step-by-step explanation:
$18,000 loan
annualend-of-year installment payments of $4,309
F = P(1+r)ⁿ
a. r = 15% = 0.15
18000 = 4309(1+0.15)ⁿ
18000/4309 = 1.15ⁿ
4.1773 = 1.15ⁿ
ln 4.1773 = ln 1.15ⁿ
ln 4.1773 = n*ln 1.15
n = ln 4.1773/ln 1.15
n = 10.2 years
b. r = 12% = 0.12
18000 = 4309(1+0.12)ⁿ
18000/4309 = 1.12ⁿ
4.1773 = 1.12ⁿ
ln 4.1773 = ln 1.12ⁿ
ln 4.1773 = n*ln 1.12
n = ln 4.1773/ln 1.12
n = 12.6 years
c. r = 19% = 0.19
18000 = 4309(1+0.19)ⁿ
18000/4309 = 1.19ⁿ
4.1773 = 1.19ⁿ
ln 4.1773 = ln 1.19ⁿ
ln 4.1773 = n*ln 1.19
n = ln 4.1773/ln 1.19
n = 8.2 years
d. The general relationship is n = ln 4.1773/ln (1+r) r as a decimal
is 0 not an element of an empty set?
Answer:
0 is not an element of an empty set.
Step-by-step explanation:
We are asked to determine whether 0 is not an element of an empty set.
We know that an empty set is an unique set having no elements. The cardinality of an empty set is 0.
Cardinality stands for the count of element is an set. An empty set is denoted by symbols ∅ or { }.
The empty set is like an empty container. The container is there, but nothing is in it.
When 0 is an element of a set, then its cardinality would be 1.
Therefore, 0 is not an element of an empty set.
A realty company looks at a recent sample of houses that have sold On testing the nul hypothesis that 57% of the houses take more than three months to sell against the hypothesis that more than 57% of the houses take more than three months to sell, they find a P value of 0.026 which conclusion is appropriate? Explain.
Choose the correct answer below. A. If 57% of the houses take more than three months to sell, there is a 2 6% chance that a random sample proportion would be as high as or higher than the one they obtained B. There is a 26% chance that 57% of the houses take more than 3 months to sell C. There is a 97 4% chance that 57% of the houses take more than 3 months to sell D. There is a 26% chance that the null hypothesis is correct
If 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained.
Explanation:The appropriate conclusion is that if 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained. This means that the result is statistically significant, indicating that the proportion of houses that take more than three months to sell is likely higher than 57%.
Two companies have sent representatives to an industry conference. The first company sent 12 representatives and the second company sent 20 representatives. Only 22 will be given the chance to make presentations. What is the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen?
Final answer:
The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is about 1.288%, calculated using the hyper geometric probability formula.
Explanation:
The question asks for the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen to make presentations at an industry conference. This can be solved using the hypergeometric probability distribution since we are dealing with two groups and selections without replacement. The first group (G1) consists of 12 representatives from the first company, and the second group (G2) consists of 20 representatives from the second company.
The formula for calculating hyper geometric probability is:
[tex]P(X = k) = (C(G1, k) * C(G2, n - k)) / C(G1 + G2, n)[/tex]
Where:
C(G, k) is the combination of k items from a group G.X is the random variable representing the number of successes (in this case, representatives from G1 chosen).k is the number of successes desired (10 representatives from G1).n is the total number of draws (22 representatives in total).To find the probability, we calculate:
[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]
Plugging in the values gives us:
[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]
= [tex](66 * 125,970) / 645,122,40[/tex]
=[tex]8,309,820 / 645,122,40[/tex]
=[tex]0.01288 or 1.288%[/tex]
Therefore, the probability that exactly 10 representatives from the first company and 12 from the second will be chosen is about 1.288%.
The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is approximately 0.0716%. This is calculated using the combination formula and the hypergeometric distribution.
We will use the concept of combinations and the hypergeometric distribution.
The total number of ways to select 22 representatives out of 32 (12 from the first company and 20 from the second company) is given by the combination formula [tex]\( C(n, k) = \frac{{n!}}{{k!(n-k)!}} \)[/tex] . This reflects the entire sample space.
The number of ways to choose 10 representatives out of 12 from the first company is C(12, 10).The number of ways to choose 12 representatives out of 20 from the second company is C(20, 12).Therefore, the probability P is calculated as:
[tex]\[ P = \frac{{C(12,10) \times C(20,12)}}{{C(32,22)}} \][/tex]
Using a calculator or computing these values manually, we find:
C(12,10) = 66
C(20,12) = 125,970
C(32,22) = 1,166,803,110
Thus, the probability P becomes:
[tex]\[ P = \frac{{66 \times 125,970}}{{1,166,803,110}} \][/tex]
After computation, we get:
[tex]\[ P \approx 0.000716 \][/tex]
Therefore, the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen is approximately 0.000716, or 0.0716%.
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $1200. It's original price is $1400. What percent of the original price will you save if you purchase it?
Answer:
If you purchase it, you will save 16.67% of the original price.
Step-by-step explanation:
Percentage problems can be solved as a simple rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
A percentage problem is an example where the relationship between the measures is direct.
The problem states that the model you really like happens to be on sale for $1200 and it's original price is $1400. It means the you saved $1400-$1200 = $200. Thus, the problem wants to know how much $200 is of $1200. So, we have the following rule of three
$1200 - 100%
200 - x%
1200x = 200*100
[tex]x = \frac{20000}{1200}[/tex]
x = 16.67%.
If you purchase it, you will save 16.67% of the original price.